Magnetic fasteners commonly employ a relatively thin circular disk of magnetic material the upper face of which is a north pole and the lower face of which is a south pole. Flux from the upper north pole passes upwardly to an armature made of a permeable material; and the flux entering the armature is returned to the lower south pole either through a central rod of permeable material or the peripheral rim of a cup in which the permanent magnet is mounted. The peripheral rim of the permeable cup or the central permeable rod has an area appreciably less than that of either of the faces of the permanent magnet. The high flux concentration in either the annular rim of the cup or the central rod provides the essential holding force for the magnetic fastener against the armature.